Analyzing multiparticle quantum states: problems and some solutions
Prof. Dr. Otfried Gühne (Fachbereich Physik der Universität Siegen)

Many experiments nowadays aim at the observation of quantum phenomena with several particles, such as trapped ions or polarized photons. In my talk I present results on three problems concerning the characterization of multiparticle quantum states. First, in many experiments one measures certain observables in order to determine the quantum state completely. The resulting state, however, has often unphysical properties (such as negative eigenvalues). This can be due to systematic errors, such as a misalignment of the measurement directions, or due to statistical fluctuations coming from the finite number of experiments. I will introduce a method to distinguish such statistical errors from systematic errors and apply the method to data obtained in a ion-trap experiment [1].

Second, if measurement data without systematic errors are given, the task remains to reconstruct a density matrix. I will show that the frequently used methods of maximum likelihood reconstruction and free least squares optimization lead to a systematic bias, underestimating the fidelity and overestimating the entanglement.
This is shown to be a fundamental problem for any state reconstruction scheme that results always in valid density operators [2].

Finally, if in an experiment the quantum state has been reconstructed properly, the question remains how to characterize its correlations.
I will introduce a method based on exponential families, which leads to a natural extension of the concept of multiparticle entanglement.
This approach can, for instance, be used to verify the presence of complex interactions in experiments for quantum simulation.

[1] T. Moroder et al., Phys. Rev. Lett. 110, 180401 (2013).
[2] C. Schwemmer et al., arXiv:1310.8465.
[3] S. Niekamp et al., J. Phys. A: Math. Theor. 46, 125301 (2013).